MABE Department, Center for Musculoskeletal Research, University of Tennessee, Knoxville, TN.
J Arthroplasty. 2020 Nov;35(11):3289-3299. doi: 10.1016/j.arth.2020.06.017. Epub 2020 Jun 14.
Mathematical modeling is among the most common computational tools for assessing total knee arthroplasty (TKA) mechanics of different implant designs and surgical alignments. The main objective of this study is to describe and validate a forward solution mathematical of the knee joint to investigate the effects of TKA design and surgical conditions on TKA outcomes.
A 12-degree of freedom mathematical model of the human knee was developed. This model includes the whole lower extremity of the human body and comprises major muscles and ligaments at the knee joint. The muscle forces are computed using a proportional-integral-derivative controller, and the joint forces are calculated using a contact detection algorithm. The model was validated using telemetric implants and fluoroscopy, and the sensitivity analyses were performed to determine how sensitive the model is to both implant design, which was analyzed by varying medial conformity of the polyethylene, and surgical alignment, which was analyzed by varying the posterior tibial tilt.
The model predicted the tibiofemoral joint forces with an average accuracy of 0.14× body weight (BW), 0.13× BW, and 0.17× BW root-mean-square errors for lateral, medial, and total tibiofemoral contact forces. With fluoroscopy, the kinematics were validated with an average accuracy of 0.44 mm, 0.62 mm, and 0.77 root-mean-square errors for lateral anteroposterior position, medial anteroposterior position, and axial rotation, respectively. Increasing medial conformity resulted in reducing the paradoxical anterior sliding midflexion. Furthermore, increasing posterior tibial slopes shifted the femoral contact point more posterior on the bearing and reduced the tension in the posterior cruciate ligament.
A forward solution dynamics model of the knee joint was developed and validated using telemetry devices and fluoroscopy data. The results of this study suggest that a validated mathematical model can be used to predict the effects of component design and surgical conditions on TKA outcomes.
数学建模是评估不同植入物设计和手术对准的全膝关节置换术（TKA）力学的最常用计算工具之一。本研究的主要目的是描述和验证膝关节的正向解决方案数学模型，以研究 TKA 设计和手术条件对 TKA 结果的影响。
开发了一个具有 12 个自由度的人体膝关节数学模型。该模型包括人体下肢的整个下肢，包括膝关节的主要肌肉和韧带。肌肉力量使用比例积分微分控制器计算，关节力使用接触检测算法计算。该模型使用遥测植入物和荧光透视进行验证，并进行了敏感性分析，以确定模型对植入物设计的敏感性，这是通过改变聚乙烯的内侧一致性来分析的，以及手术对准的敏感性，这是通过改变胫骨后倾角来分析的。
模型预测的胫骨股骨关节力具有平均精度为 0.14×体重（BW），0.13× BW 和 0.17× BW 根均方误差用于外侧，内侧和总胫骨股骨接触力。使用荧光透视，运动学验证的平均精度为 0.44 毫米，0.62 毫米和 0.77 根均方误差用于外侧前后位置，内侧前后位置和轴向旋转。增加内侧一致性会减少中屈时的反常前滑动。此外，增加胫骨后倾斜率会使股骨接触点更向后移动在轴承上，并减少后交叉韧带的张力。
使用遥测设备和荧光透视数据开发并验证了膝关节的正向解决方案动力学模型。本研究的结果表明，经过验证的数学模型可用于预测组件设计和手术条件对 TKA 结果的影响。
